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Question

A bullet of mass a and velocity b is fired into a large block of wood of mass c, what is the final velocity of the system?


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Solution

Step 1: Given

Mass of the bullet=a

Initial velocity of the bullet=b

Mass of the wood=c

Step 2: Determine the initial momentum

Let the initial momentum be Mi

Mi=mass×initialvelocity=ab

Step 3: Determine the final momentum

Let the final velocity be v and the final momentum be Mf

Mf=massofbulletinwood×finalvelocity=(a+c)v

Here, both the mass of the bullet and the mass of wood are considered as the bullet enters the wooden block

Step 4: Determine the final velocity

According to the law of conservation of momentum, the initial momentum will be equal to the final momentum.

Mi=Mfab=(a+c)vv=ab(a+c)

Therefore, the final velocity of the system is v=ab(a+c)


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